How to solve 1/2 * x = sqrt(x)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 1/2 * x = sqrt(x) | Equatix

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Question

$$\frac{1}{2}x=\sqrt{x}$$

Solve for x

$x=0$
$x=4$

Solution Steps

Square both sides of the equation.

$$\left(\frac{1}{2}x\right)^{2}=\left(\sqrt{x}\right)^{2}$$

Expand $\left(\frac{1}{2}x\right)^{2}$.

$$\left(\frac{1}{2}\right)^{2}x^{2}=\left(\sqrt{x}\right)^{2}$$

Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.

$$\frac{1}{4}x^{2}=\left(\sqrt{x}\right)^{2}$$

Calculate $\sqrt{x}$ to the power of $2$ and get $x$.

$$\frac{1}{4}x^{2}=x$$

Subtract $x$ from both sides.

$$\frac{1}{4}x^{2}-x=0$$

Factor out $x$.

$$x\left(\frac{1}{4}x-1\right)=0$$

To find equation solutions, solve $x=0$ and $\frac{x}{4}-1=0$.

$$x=0$$ $$x=4$$

Substitute $0$ for $x$ in the equation $\frac{1}{2}x=\sqrt{x}$.

$$\frac{1}{2}\times 0=\sqrt{0}$$

Simplify. The value $x=0$ satisfies the equation.

$$0=0$$

Substitute $4$ for $x$ in the equation $\frac{1}{2}x=\sqrt{x}$.

$$\frac{1}{2}\times 4=\sqrt{4}$$

Simplify. The value $x=4$ satisfies the equation.

$$2=2$$

List all solutions of $\frac{x}{2}=\sqrt{x}$.